Problem: Simplify the following expression: $k = \dfrac{9x^2 - 27x - 90}{x + 2} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $9$ , so we can rewrite the expression: $ k =\dfrac{9(x^2 - 3x - 10)}{x + 2} $ Then we factor the remaining polynomial: $x^2 {-3}x {-10} $ ${2} {-5} = {-3}$ ${2} \times {-5} = {-10}$ $ (x + {2}) (x {-5}) $ This gives us a factored expression: $\dfrac{9(x + {2}) (x {-5})}{x + 2}$ We can divide the numerator and denominator by $(x - 2)$ on condition that $x \neq -2$ Therefore $k = 9(x - 5); x \neq -2$